Concerning the instantaneous mass and the extent of an expanding universe

Abstract

Key words cosmology: mass of the universe -cosmology: cosmic densityIn this article we want to answer the cosmologically relevant question what, with some good semantic and physical reason, could be called the mass Mu of an infinitely extended, homogeneously matter-filled and expanding universe. To answer this question we produce a space-like sum of instantaneous cosmic energy depositions surrounding equally each spacepoint in the homogeneous universe. We calculate the added-up instantaneous cosmic energy per volume around an arbitrary space point in the expanding universe. To carry out this sum we use as basic metrics an analogy to the inner Schwarzschild metric applied to stars, but this time applied to the spacepoint-related universe. It is then shown that this leads to the added-up proper energy within a sphere of a finite outer critical radius defining the point-related infinity. As a surprise this radius turns out to be reciprocal to the square root of the prevailing average cosmic energy density. The equivalent mass of the universe can then also be calculated and, by the expression which is obtained here, shows a scaling with this critical radius of this universe, a virtue of the universe which was already often called for in earlier works by E. Mach, H. Thirring and F. Hoyle and others. This radius on the other hand can be shown to be nearly equal to the Schwarzschild radius of the so-defined mass Mu of the universe.

About universes with scale‐related total masses and their abolition of presently outstanding cosmological problems

“…The latter fact by the way has been emphasized as true for completely different reasonings, eg. by Einstein (1920), Dirac (1937), Whitrow (1946), Hoyle (1990Hoyle ( , 1992, Fahr (2006), Fahr & Heyl (2006) and Fahr & Zoennchen (2006). The above derived result finally challenges to put the question of how large the mass of the universe under these auspices might have been at the very early cosmic time, when the radius of the universe amounted to one Planck scale R Pl = hG/c 3 of a Planck mass m Pl = hc/G.…”

“…In this respect R u can be called the distance between two arbitrary space points comoving with the Robertson-Walker-like homologous cosmological expansion of the universe, validating the relationṘ u /R u =Ṡ/S, if S for instance is the distance between any two freely comoving galaxies (dots on top of quantities mean derivatives with respect to cosmic time). This relation was already suggested by considerations carried out by Kolb (1989), Overduin & Fahr (2001 or Fahr & Heyl (2006). A detailed justification for such a scaling behaviour will be provided in Sect.…”

Revised Concepts for Cosmic Vacuum Energy and Binding Energy: Innovative Cosmology

“…As evident from the above expression no real matter can be summed-up anymore from beyond the "local Schwarzschild infinity" (i.e. "point-associated Schwarzschild mass horizon", see Fahr & Heyl (2006)) which is at a distance…”

A New Cosmological Model

“…which is a general expression of Mach's principle (Assis, 1994;Brans & Dicke, 1961) showing that our model can fulfil the principle of equivalence of rotation (Fahr & Heyl, 2006). It is often useful to introduce the critical density ρ c : and the density parameter Ω (we take the effects of a cosmological constant into account by including the vacuum energy density ρ Λ = Λ/8πG into the total density).…”

“…That result could appear surprising, but, as explained in , it has yet been emphasized as possibly true from completely different reasonings by many physicists (Dirac, 1937;Einstein, 1917;Fahr & Heyl, 2006;Fahr & Zoennchen, 2006;Hoyle, 1990;1992;Whitrow, 1946). It moreover appears, on one hand, that a scaling of masses with the cosmic scale factor is the most natural scale required to make the theory of general relativity conformally scale-invariant (H. Weyl's…”